No matter what I try, even with programs such as Resource Hacker, I can't change the GoG circular icon that shows for any games I've installed. Delete the .ico file just results in the default blank page icon, and launching via the original .exe also changes nothing. Would it be possible to change them at all?

Never mind, you can swap it out by modifying the GoG .exe, but launching via the original .exe still keeps the GoG icon.